A two-step stochastic model of anaerobic digestion

Abstract

This paper deals with a stochastic model of the so-called Anaerobic Model number 2. Here the maximal growth rate of the acidogenic microorganisms is affected by a white noise in environment. As far as the mathematical analysis of this model is concerned, we first use the Itô formula to investigate the existence and uniqueness of the global positive solution. Then, we explore and derive the conditions of persistence and extinction of the microorganisms. Finally, by performing some numerical simulations, we illustrate the theoretical results obtained.